Trajectory planning with flexible replanning functionality - changed end point

ABSTRACT

An improved method for controlling a lifting device, which moves a load along a first movement direction and along a second movement direction within a specified working area of the lifting device from a starting point to an end point. Individual movements are planned for the first movement direction and for the second movement direction, by which the load is moved further along the movement directions and brought to a newly specified end point.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority under 35 U.S.C. § 119(a) to Austria Application No. A50960/2021 filed Nov. 30, 2021, the disclosure of which is expressly incorporated by reference herein in its entirety.

BACKGROUND 1. Field of the Invention

The present invention relates to a method for controlling a lifting device that moves a load along a first direction of movement and along a second direction of movement within a specified working area of the lifting device in accordance with a specified trajectory from a starting point to an end point.

2. Discussion of Background Information

The planning of suitable trajectories is often an essential part of operational and problem-solving concepts in a wide variety of technical applications. Here, a trajectory is understood to be the temporal profile of the movement of a body along a curve, a path or a way, which in the case of a rigid body can be described, for example, by the position profile of its center of gravity. The common use of the term “trajectory” in control engineering as a temporal (reference) profile of state or output variables of a (technical) system to be controlled deviates from this definition, but does not contradict it. If a technical problem requires on the one hand the planning of a movement of a physical body, but on the other hand also the realization of the planned movement, for example by suitable control or regulation of drive elements provided for this purpose, the mentioned meanings of the term “trajectory” coincide, which is the case in many applications and also in the context of the following explanations.

Trajectory planning as described above is a basic sub-task in the automation of vehicles, such as passenger cars or trucks. With the help of map- or sensor-based data, trajectories, which primarily describe the movement of a vehicle on a road, are first planned and then implemented by the control of the vehicle as set point variables. In addition to convenience aspects, feasibility and collision-free nature of a trajectory are often important criteria when implementing this approach.

Another area in which the topic of trajectory planning is of great importance is the field of transport logistics. In order to increase the efficiency of logistics processes, among other things, rapid goods turnover is required in this division. This results in particular in requirements for rapid loading and unloading operations of cargo ships, as well as correspondingly rapid movement operations of lifting devices used for loading and unloading. Such lifting devices are also increasingly being operated in automated mode, wherein demands for fast movement operations are directly reflected in the trajectories to be implemented in (automated) operation.

Lifting devices are available in a wide variety of embodiments, which are accordingly used in a wide variety of applications. For example, there are tower cranes, which are mainly used for building construction and civil engineering, or mobile cranes, e.g., for the assembly of wind turbines. Furthermore, bridge cranes are used, e.g., as indoor cranes in factory halls, or gantry cranes e.g., for the manipulation of transport containers at handling locations for the intermodal handling of goods. Goods to be transported are mainly stored in standardized containers, so-called ISO containers, which are equally suitable for the transport modes road, rail and water. Objects to be transported by a lifting device, such as a group of containers with goods contained therein, are hereinafter referred to simply as “load” or “loads”.

The design and mode of operation of gantry cranes in particular are well known and are described, for example, in US 2007/0289931 A1 on the basis of a “ship-to-shore crane” (STS crane). A gantry crane has a supporting structure, or gantry, on which a boom is arranged. Here, the gantry with wheels is movably arranged on a track, for example, and can be moved in one direction. The boom is fixed to the gantry and usually has a trolley that moves along the boom. To pick up a load, such as an ISO container, the trolley is usually connected by four ropes to a load receiving element known as a spreader. To pick up and manipulate a container, the spreader can be raised or lowered by winches. The spreader can also be adapted to containers of different sizes.

Typically, cranes are operated by a crane operator, who usually controls the movement of a crane from a cabin. Such a cabin can be arranged on a gantry or on a movable trolley. For precise and collision-free manipulation of loads, high demands are placed on the crane operator, which is why a training period of at least one year is usually necessary. In particular, the rapid movement of loads with small pendulum movements represents a highly complex activity, which is why several years of practical experience is usually required to successfully perform the job of a crane operator. The job of a crane operator is often made more difficult by a high level of physical stress, due among other things to the high level of concentration required in conjunction with sitting for long periods with the gaze tilted downward. For these reasons, among others, it is a declared goal of automation technology to at least partially automate the complex manipulation procedures of a lifting device and thus simplify them for the crane operator. Inseparably linked to the automated operation of lifting device is the planning of suitable trajectories to be implemented by the lifting device in automated operation.

One issue that has received little attention to date, but is becoming increasingly important, is the replanning of existing trajectories. An example relevant to practice, in which the requirement for trajectory replanning increasingly occurs, is the STS (“Ship-to-Shore”) cranes already mentioned. As mentioned, the primary purpose of STS cranes is to load containers from cargo ships onto trucks for onward transportation or onto so-called “automated guided vehicles”. It is often the case that a truck has not yet arrived in an area that can be reached by the lifting device or crane, but the movement of the load must already be started for reasons of efficiency. For obvious reasons, the actual position of a truck for load pickup can only be recorded and subsequently taken into account after its arrival. In order to be able to start the movement of a container or a load even before the truck arrives, it is necessary in such cases to first assume a suitable target position for the planning of a first trajectory and to adjust the assumed target position to the true target position later in the course of replanning.

Basically, the constant increase in the speed of transport processes often leads to situations in which trajectories must first be planned under certain assumptions in order to be able to start a transport process as early as possible. If, for example, assumptions made with regard to the target position do not subsequently occur, it is usually necessary to replan or change a trajectory. Although the topic of trajectory planning for lifting devices is addressed in the prior art, issues regarding trajectory replanning have hardly been mentioned in the relevant literature so far.

For example, EP 3461783 BI describes the determination of a trajectory for the movement of a load by a lifting device. For this purpose, a geometric path on the one hand and a dynamic path on the other hand are calculated, which are combined in a further step to generate a trajectory. A disadvantage of this approach is the large computational effort associated with it. A (real-time capable) replanning during the operation of a lifting device is thus only possible to a limited extent.

CN 111170153 A, on the other hand, describes a method for replanning a given trajectory on the basis of obstacles detected by measurement. The necessary measurement requirements represent a significant complication for the implementation of this method. Furthermore, CN 111170153 A does not describe how changed end points can be taken into account and, moreover, does not make any statements on the real-time capability of the method described.

In addition, the known prior art shows a plurality of further disadvantages, such as the usually given necessity that no changes of direction along the given movement directions must result from a replanning. A further essential point is the real-time capability of concepts for trajectory replanning. Since the described replanning usually has to be done during the operation of a lifting device, the computational effort associated with replanning must not interfere with the operation of a lifting device. This aspect is also not considered in the prior art.

SUMMARY

Accordingly, it is an object of the present invention to provide an improved trajectory replanning method for a lifting device that enables efficient replanning of a trajectory along which a load is moved, taking into account a variable end point.

This object is solved by the present invention. In this case, the lifting device is assumed to be one that moves a load along a first movement direction and along a second movement direction within a specified working area of the lifting device in accordance with a specified trajectory from a starting point to an end point.

According to the invention, the end point for this lifting device is changed to a new end point at a command time point during the movement of the load, wherein, taking into account specified kinematic constraints of the lifting device an individual movement is planned for the first movement direction and for the second movement direction respectively, which determines the further movement of the load along the respective movement direction from the command time point onwards, wherein the individual movements each end in a projection of the changed end point onto the respective direction of movement, and wherein the planned individual movements are executed in accordance with a specified movement sequence in order to further move the load along the first direction of movement and along the second direction of movement in accordance with a replanning trajectory resulting from the movement sequence of the planned individual movements. By planning individual movements, the numerical complexity is significantly reduced herein compared to methods known from the prior art, enabling efficient and flexible replanning even during operation of a lifting device.

In an advantageous manner, the individual movements planned for the first movement direction and those planned for the second movement direction are planned as independent individual movements, which means that no mutual dependencies need to be taken into account and the actual replanning task can be simplified even further.

In a further advantageous embodiment of the present invention, the position profiles of the load specified by the planned individual movements are specified as position profiles that can be continuously differentiated in time at least four times. In this manner, swinging of the moving load can be avoided in a remarkable way due to the principle.

In a further advantageous embodiment of the present invention, the position profiles specified by the individual movements are filtered by a filter with a predeterminable time constant in order to generate the temporally at least four times continuous differentiability. In this manner, it can be ensured in a particularly advantageous manner that predefined kinematic constraints of the lifting device are adhered to. The time constant of the filter can here be made dependent on the geometry of the lifting device in an advantageous manner to enable precise matching to the given lifting device.

In a further advantageous embodiment of the present invention, in the case of an obstacle located between the position taken on by the load at the command time point and the new end point, a second individual movement is planned for the second movement direction to move the load around the obstacle. It should be noted here that in order to go around an obstacle, it is usually necessary to combine the individual movement planned for going around with other individual movements planned along the other movement directions, i.e., to suitably combine horizontal and vertical movements. In this case, it may be necessary to coordinate or adapt the new individual movement to any other individual movements that may already exist. In the described manner, the load can be moved around the obstacle and collisions of the load with the specified obstacle can be avoided.

In a further advantageous embodiment of the present invention, the sequence of movements mentioned provides for an alternating start and, if necessary, overlapping execution of the planned individual movements along the first movement direction and of individual movements along the second movement direction, as a result of which, on the one hand, obstacles can be avoided and, on the other hand, time can be saved to a partly significant extent.

Furthermore, prior to the execution of at least one planned individual movement, the method according to the invention allows checking whether the expected replanning trajectory leads to a collision of the load with an obstacle specified in the working area. This check can be performed in an advantageous manner by comparing the collision times at which the respective individual movements reach projections onto the corresponding movement direction of a keypoint derived from the specified obstacle, wherein a numerical root finding method can be used to determine these collision times at which the respective individual movements reach projections onto the corresponding movement direction of a keypoint derived from the specified obstacle. In this manner, obstacles in the working area of the lifting device can be included in the replanning according to the invention, and possible collisions can be reacted to in good time. It should be noted that the procedure according to the invention allows the described check to be performed in a particularly efficient manner.

If a possible collision is detected by the described anticipatory calculation, at least one individual movement cannot be executed and instead, along the movement direction for which the at least one non-executed individual movement has been planned, a specified braking operation can be executed for at least the duration of a specified minimum braking time. Thus, on the one hand, collisions can be avoided in an advantageous manner, and on the other hand, a new starting situation is created in the described manner, from which a renewed replanning of individual movements is made possible.

According to the preceding explanations, a new individual movement can be planned for the corresponding movement direction in an advantageous manner instead of the at least one individual movement that has not been executed, wherein a replanning trajectory to be expected by the at least one new individual movement is determined and it is checked whether the replanning trajectory to be expected leads to a collision of the load with an obstacle specified in the working area, and wherein the new individual movement is executed if no collision is detected, or the specified braking operation is continued for at least one further minimum braking time, and a replanning of an individual movement as well as a check of the replanning trajectory, which is to be expected by the newly planned individual movement, is performed again if a new collision with an obstacle is detected. In this manner, the method according to the invention can be continued without collision, even if a first replanning would have led to a collision, and it can be ensured that there is no collision of the transported load with obstacles during the entire movement of the load.

Further, in support of the present invention, the position of the load can be measured and the measurement of the position of the load can be used in performing the individual movements. The use of measurement data is usually particularly advantageous for the implementation of planned individual movements by control technology.

Furthermore, it should be noted that the method according to the invention is by no means limited to movements in a plane, and that movements in (three-dimensional) space can also be planned by the present invention. In the case of more than two dimensions, the properties of the inventions at issue have an even more advantageous effect. Here, the independence of the planned individual movements should be especially emphasized, in particular since three interdependent coordinates would further increase the complexity to be mastered in replanning—compared to the already challenging 2D case.

Other exemplary embodiments and advantages of the present invention may be ascertained by reviewing the present disclosure and the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the present invention is described in greater detail with reference to FIGS. 1 to 6 , which, by way of example, show advantageous embodiments of the invention in a schematic and non-limiting manner. The drawings show:

FIG. 1 a schematic representation of a container crane with a trajectory within a working area of the container crane.

FIG. 2A a possible sequence of the method according to the invention when a modified end point is specified,

FIG. 2B an individual movement in X-direction.

FIG. 2C an individual movement in Y-direction,

FIG. 3A a time-optimal individual movement for one movement direction,

FIG. 3B a block diagram for filtering the position, velocity and acceleration profiles belonging to an individual movement,

FIG. 4 a trajectory and a replanning trajectory within a working area with a prohibition zone,

FIG. 5A individual movements in the X-direction when performing a braking operation according to the invention,

FIG. 5B individual movements in the Y-direction when performing a braking operation according to the invention,

FIG. 5C resulting trajectories when performing a braking operation according to the invention,

FIG. 6 a replanning trajectory for collision avoidance in the presence of two obstacles.

DETAILED DESCRIPTION

The particulars shown herein are by way of example and for purposes of illustrative discussion of the embodiments of the present invention only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the present invention. In this regard, no attempt is made to show structural details of the present invention in more detail than is necessary for the fundamental understanding of the present invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the present invention may be embodied in practice.

FIG. 1 shows a lifting device 1 in the form of a schematic container crane 2, as used for loading and unloading ships in a harbor. Typically, a container crane 2 has a supporting structure 3 that is either fixed or movable on the ground. In the case of a movable arrangement, the supporting structure 3 can, for example, be arranged to move in the Z direction on rails. This degree of freedom in the Z direction means that the container crane 2 can be used flexibly in terms of location. To move the supporting structure 3 in the Z direction, for example, a suitable displacement device can be arranged on the lifting device, e.g., driven wheels, a cable pull, a gear drive or similar. The supporting structure 3 has a boom 4 that is fixedly connected to the supporting structure 3 at a certain height yr.

A running element 5 is usually arranged on this boom 4, which is movable in the longitudinal direction of the boom 4, i.e., in the X-direction in the example shown. Accordingly, a running element 5 can be mounted in guides by rollers. A running element drive, not shown, is provided for the running element 5 in order to move the running element 5 in the X-direction. The running element drive can be provided on the running element 5 itself, but can also be arranged on the boom 4 or on the supporting structure 3. The running element 5 is usually connected by retaining elements 6 to a load receiving element 7 for receiving a load 8. In the case of a container crane 2, the load 8 is typically a container 9, in most cases an ISO container 20, 40 or 45 feet long, 8 feet wide and 8 feet, 6 inches high.

The retaining elements 6 are usually in the form of ropes, wherein in most cases four retaining elements 6 are arranged on the running element 5, but more or fewer retaining elements 6 can also be provided, in the simplest case also only a single retaining element 6. To accommodate a load 8, such as a container 9, the distance between the running element 5 and the load receiving element 7 can be adjusted by a lifting drive (not shown), thus in the Y-direction in FIG. 1 . If the retaining elements 6 are ropes, the lifting height is usually adjusted by one or more rope winches. The area in which a lifting device 1 can move a load 8 is referred to in the present context as the working area 15. Depending on the size and design of the lifting device 1, the working area 15 may vary.

In the situation shown in FIG. 1 , the objective is to move load 8 from starting point A to end point E. When loading a ship, the starting point A may be, for example, a position of a container 9 on land, such as on a truck trailer, a rail car, or a storage yard, and the end position E may be, for example, a specified position of the container 9 on a ship. In an advantageous manner, the working area 15 can here be defined in a plane or also in the entire movement space and it can be checked whether a specified starting point A as well as a specified end point E lie within the working area 15 and whether accordingly a continuous movement of the load 8 from the starting point A to the end point E is possible.

In order to move a load 8 along a trajectory T from the starting point A to the end point E, the lifting device 1 has a crane controller 16 with a computing unit 12, for example in the form of an electronic control unit in the form of suitable hardware and/or software, by which the movement of the load 8 along the respective movement direction X, Y. Z can be controlled. If a starting point A and/or end point E is defined manually by a user, for example, the starting point A and/or end point E can be transmitted to the computing unit 12, for example, via a suitable interface. A starting point A and/or an end point E can also be determined in the computing unit 12. Possible implementations of a computing unit 12 include microprocessor-based hardware, microcontrollers, and integrated circuits (ASIC. FPGA). The crane controller 16 communicates with the drives provided for this purpose, such as a running element drive or a winch, in order to control and/or regulate the movement of the load 8, and is typically designed to be able to detect the current position of the running element 5, the position of the load receiving element 7 and, if necessary, the position of the supporting structure 3.

In this sense, in the situation shown in FIG. 1 , the coordinates of the central point P_(Z), which is located on the upper side of the load receiving element 7 facing the boom 4, can be detected in the X-Y plane E_(XY) using the coordinates x_(L) and y_(L) of the load receiving element 7, but it is also possible to detect the coordinates x_(T) and y_(T) of the running element 5 in both the X- and Y-directions. The central point P_(Z) can be used to describe the position of the load 8 and can therefore also be understood as the load position. Furthermore, the position y_(T) of the running element in the Y-direction is often determined by the design height of the supporting structure 3 or the boom 4 and is therefore constant. The coordinates are related to a given coordinate system. When the load 8 moves in the Z direction, that is, when the supporting structure 3 of the lifting device 1 moves in the Z direction, the position z_(L) of the load receiving element 7 and the position z_(T) of the running element 5 would also be detected in the Z direction.

From a trajectory T along which the load 8 is moved, a rapid transfer of the load 8 from the starting point A to the end point E is usually required. As explained at the beginning, during such a transfer it may become necessary for several reasons to adapt a given trajectory T during the movement of the load 8 to changing circumstances in the area of the lifting device 1, i.e., to replan the trajectory T. This problem is solved by the method according to the invention. How the method according to the invention can be used to replan a trajectory T taking into account a changed end point E_(n) is specifically shown in FIGS. 2A-2C.

Here, three situations are plotted along the time axis t, which can occur during the application of the method according to the invention during the movement of a load 8 by a lifting device 1 along a first and along a second movement direction, in this case along the movement directions X and Y. In the situation shown in FIG. 2A, the movement of the load 8 starts at the starting point A at the time t_(A). The position of the load 8 is thereby equated to the previously mentioned central point P_(Z) and accordingly also designated as P_(Z). At time point t_(A), the load 8 starts to move along the specified trajectory T shown in dashed lines in FIG. 2A, wherein the position P_(Z) of the load 8 and the starting point A initially overlap.

At time point t_(K), hereinafter also referred to as command time point t_(K), a new end point E_(n) is now specified to which load 8 is to be transferred instead of the previous end point E. The command time point t_(K) can be specified by an operator, such as a crane operator, and can therefore be selected as freely as possible. However, the command time point t_(K) can also be generated internally in the computing unit 12. Also, several successive command time points t_(K) for a repeated change of an end point E are conceivable. At command time point t_(K), the load 8 is at position P_(z)(t_(K)). According to the invention, the replanning of the movement of the load 8 is started immediately after the new end point E_(n) has been specified. This is done according to the previous explanations by projections of the position P_(z)(t_(K)) taken on by the load 8 at the command time point t_(K) and of the new end point E_(n) onto the movement directions X, Y. The projections of the position P_(z)(t_(K)) taken on by the load 8 at the command time point t_(K) and of the new end point E_(n) onto the X-axis are called P_(Z)′ and E_(n)′, the projections onto the Y-axis are called P_(Z)″ and E_(n)″.

According to the invention, the projections P_(Z)′, E_(n)′ or P_(Z)″, E_(n)″ are considered separately. For each of the separated pairs of projections, an individual movement TE is planned to connect the respective projections P_(Z)′, E_(n)′ or P_(Z)″, E_(n)″ along the corresponding movement directions X, Y. An individual movement TE preferably defines a profile of position, velocity and acceleration along the respective movement direction. In this manner, for example, the projection P_(Z)′ of the load position P_(Z) is connected to the projection E_(n)′ of the end point E_(n) along the movement direction X. In this way, for each of the movement directions X, Y initially one individual movement TE results.

After planning them, the planned individual movements are executed according to a specified sequence, hereinafter referred to as “movement sequence”, to move the load 8 along the first movement direction X and along the second movement direction Y. Thus, a replanning trajectory TU results from the planned individual movements TE. The replanning trajectory TU is shown by the solid line in FIG. 2 .

By separating the new overall movement to be planned into a plurality of individual movements TE to be planned instead, the (re-)plannning task to be solved is significantly simplified compared to methods known from the prior art. Thus, the complex problem of planning at least one two-dimensional movement is reduced to planning several only one-dimensional movements.

Especially this circumstance proves to be advantageous in the practical implementation, since the planning of one-dimensional movements is a well-known problem in control and automation engineering, which has already been solved in various ways. In the concrete planning of the individual TE movements, a plurality of known approaches can thus be used. If, for example, a time-optimal transfer of the load 8 to the new end point E_(n) is to be ensured, the bang-bang controller approach, which is sufficiently known from control engineering literature, can be used, for example, using maximum accelerations along the movement directions X, Y that can be realized by the given drives of the lifting device 1.

Individual movements TE, as may occur in the method according to the invention, are shown in FIGS. 2B and 2C. Corresponding to the individual movement TE_(X) shown in FIG. 213 , in which the position profile s_(x) connects the projection P_(z)′(t_(k)) with the projection E_(n)′, the planning of an individual movement TE with regard to the temporal position profile s_(x) thereof can be performed, for example, by specifying a sigmoid-like profile, which, however, is to be understood merely as an example. Other position profiles can also be used at this point. FIG. 2C shows a corresponding individual movement TE_(Y) along the Y-direction, by which the projections P_(z)″(t_(k)) and E_(n)″ are connected to the Y-direction.

In FIG. 3A, the planning of an individual movement TE is explained in more detail using a time-optimal individual movement to connect the projections P_(Z)′ and E_(n)′. In addition to the position profile s_(X), the associated velocity profile v_(x) and the associated acceleration profile a_(X) along the X-axis are also shown. In this context, a time-optimized individual movement means the fastest possible transfer of the load 8 to the new end point E_(n) within the given dynamic limitations of the lifting device 1. The most significant dynamic limitations are kinematic constraints of the drives of the lifting device 1, such as a maximum realizable acceleration of the drives or a maximum force that can be realized by the drives. These kinematic constraints result in limitations for the accelerations of the load 8 that can be realized along the respective movement directions X, Y. The maximum possible positive acceleration of load 8 is referred to as a⁺ _(max), and the maximum possible negative acceleration of load 8 is referred to as a⁻ _(max). In this sense, the fastest possible individual movement TE along the X-axis is achieved using the maximum possible positive accelerations a⁺ _(max) and the maximum possible negative accelerations a-Mo along the X-axis.

In the example shown in FIG. 3A, the displayed position, velocity and acceleration profile can be mathematically represented as

a_(x(t)) = a_(max)⁺(σ(t − t_(k)) − σ(t − T_(a1))) + a_(max)⁻(o(t − T_(a2)) − σ(t − t_(E))) v_(x(t)) = v_(x0) + a_(max)⁺(σ(t − t_(k)) − σ(t − T_(a1))) ⋅ (t − t_(k)) + a_(max)⁺ ⋅ σ(t − T_(a1)) ⋅ (T_(a1) − t_(k)) + a_(max)⁻(σ(t − T_(a2)) − σ(t − t_(E))) ⋅ (t − T_(a2)) + a_(max)⁻(σ(t − t_(E))) ⋅ (t − T_(a2)) $s_{x(t)} = {{P_{Z}^{\prime}\left( t_{k} \right)} + {v_{x0}t} + {{a_{\max}^{+}\left( {{\sigma\left( {t - t_{k}} \right)} - {\sigma\left( {t - T_{a1}} \right)}} \right)} \cdot \frac{\left( {t - t_{k}} \right)^{2}}{2}} + {\alpha_{\max}^{+} \cdot {\sigma\left( {t - T_{a1}} \right)} \cdot \left( {T_{a1} - t_{k}} \right) \cdot \left( {t - T_{a1}} \right)} + {{a_{\max}^{-}\left( {{\sigma\left( {t - T_{a2}} \right)} - {\sigma\left( {t - t_{E}} \right)}} \right)} \cdot \frac{\left( {t - T_{a2}} \right)^{2}}{2}} + {{a_{\max}^{-}\left( {\sigma\left( {t - t_{E}} \right)} \right)} \cdot \left( {T_{a2} - t_{E}} \right) \cdot \left( {t - t_{E}} \right)}}$

Here σ(x) stands for the sigma function well known from mathematics, which takes on the value one for arguments greater than or equal to zero (x≥0), and is equal to zero otherwise, v_(x0) here stands for the initial velocity at the beginning of the individual movement. Accordingly, the planning of individual movements TE, on the basis of which a position profile s_(x), a velocity profile v_(x) and an acceleration profile a_(x) are determined, can be performed by defining functions as shown above, for example by specifying time points T_(a1) and T_(a2). In an advantageous manner, boundary conditions can also be specified for this purpose, such as s_(x)(t_(E))=E′, v_(x)(t_(E))=v_(tE). In particular, the velocity v_(tE) can be chosen equal to zero, but also different from zero.

According to the above explanations, for planning a time-optimal individual movement TE, acceleration phases with maximum positive acceleration a⁺ _(max), with maximum negative acceleration a⁻ _(max), as well as with vanishing acceleration, i.e., an acceleration a_(x)=0, must be specified. In the procedure shown in FIG. 3A, this is done by specifying time points T_(a1) and T_(a2), which limit the time of the acceleration phases mentioned. The velocity profiles v_(x) and position profiles s_(x) associated with the acceleration profile a_(x) adjust themselves according to the specified acceleration profiles. The widths of the acceleration phases limited by the time points T_(a1) and T_(a2) with accelerations different from zero are usually specified in such a manner that the resulting velocities do not exceed specified limits v⁺ _(max), v⁻ _(max). It should be noted that for the acceleration of the load 8 along the movement directions X, Y, lower (constant) values than the maximum accelerations that are possible due to the kinematic constraints of the drives can also be specified.

Kinematic and/or geometric limit values can, for example, be stored in the computing unit 12 or specified to the computing unit 12. Further kinematic limit values are preferably a maximum speed v_(Tmax) and/or a maximum acceleration a_(Tmax) of the running element 5, or a maximum speed v_(Hmax) and a maximum acceleration a_(Hmax) of the lift drive in Y-direction. A geometric limitation can be given, for example, by a maximum deflection angle Θ_(XYmax) of the load receiving element 7 in the plane E_(XY). In the case of a third movement direction of the lifting device in the Z direction, a maximum speed v_(Smax) and a maximum acceleration a_(Smax) of the supporting structure 3 can additionally be specified as kinematic limit values and a maximum deflection angle Θ_(ZYmax) of the load receiving element 7 in the plane E_(ZY) can be specified as a geometric limit value. However, in addition to planning time-optimal individual movements TE, other approaches to planning individual movements TE can also be used.

In many cases, it proves advantageous in this context to design the individual movements TE_(x), TE_(y) (and possibly TE_(z)) along the axes X, Y (and possibly Z) completely independently of one another. This means that there is no relationship between the planned individual movements TE_(x), TE_(y) (or TE_(z)) on the respective axes, which could be expressed mathematically, for example, and which, in the case of a change in the position P_(z) of the load 8 along a first movement direction, for example the X-axis, would cause a change in the position P_(z) of the load 8 also along a second movement direction, for example the Y-axis.

In other cases, again, a deliberate linking of individual movements TE may be advantageous or even necessary, for example if certain areas of the working area 15 of the lifting device 1 must be avoided, e.g., due to an obstacle 11 located there. In such cases, usually the coordinate of one movement direction may take on only certain values depending on the coordinate of another movement direction. In order to prevent the load 8 from entering a prohibited area in the working area 15, such dependencies must be taken into account and the individual movements must therefore be designed to be interdependent.

The planned individual movements TE are subsequently executed as mentioned either simultaneously or offset in time to one another in order to bring the load 8 to the new end point E_(n). Staggering planned individual movements TE may be necessary, particularly in the case of prohibited areas V_(i) or obstacles 11 described above. For example, it may be necessary to delay the start of a lowering movement in the Y-direction in order to drive around an obstacle 11. An individual movement TE_(Y) planned in the Y-direction would therefore only be started with a time delay after the individual movement planned in the X-direction has already been started. The specification of which individual movement TE is to be executed first and which individual movement TE is to be executed later, if necessary, is expressed in the context of the present invention by a so-called movement sequence, which can be specified, for example, to the crane controller 16 or to the computing unit 12 provided in the crane controller 16 via a suitable interface. A movement sequence can thus be stored in the computing unit 12. A movement sequence thus defines the order in which the planned individual TE movements are to be executed. For example, a movement sequence might be: “First horizontal movement in X-direction, only then vertical movement in Y-direction.” A movement sequence can also be in the form of a table in which TE start times are assigned to the planned individual movements at which they are started. A movement sequence can also comprise time intervals that define waiting times that must at least be provided between the start times of successive individual movements TE.

A central problem in the manipulation of loads 8 by lifting devices 1, which in many cases can either be solved, but usually at least greatly reduced, by suitable trajectory planning, is the problem of load swing. In particular, rapid movement operations of lifting devices can often excite undesirable swinging and/or swaying movements of transported loads 8 or of load receiving elements. Swinging of loads 8 can in turn delay handling and manipulation procedures, since loads such as containers often cannot be placed at all in such cases, or at least not with sufficient precision, and it is necessary to wait until a given swinging has subsided again. In FIG. 1 , the possibility of forming swinging and/or pendulum movements is shown by a double arrow in the X-Y plane E_(XY).

In the present context, it is shown that so-called flat trajectories, i.e., trajectories which can be continuously differentiated a sufficient number of times depending on the concrete design of the lifting device, are effective against (load) swinging and/or pendulum movements. This approach is based on the fact that a lifting device 1 as shown in FIG. 1 is a “flat system” in the control engineering sense. Flat systems are known to have a so-called flat output.

Flat outputs and their derivatives allow, in the case of a flat system such as the lifting device 1 under consideration, the representation (also “parameterization”) of the internal state or system variables of the flat system. The internal state or system variables of a flat system can thus be represented as functions of the flat outputs and their derivatives, which, of course, the person skilled in the art of control engineering knows about. For the suppression of swinging of a load 8 transported by a lifting device 1, the fact that (in an ideal consideration) a control system constructed with the aid of a flat output cannot excite any swinging or pendulum movements of the load is of importance at this point.

In the case of the lifting device 1 considered here, the position profiles of the load 8 along the movement directions X, Y represent flat outputs of the system “lifting apparatus” 1. Here it is shown that for the suppression of swinging and/or pendulum movements it is sufficient to specify the position profiles s_(x)(t), s_(y)(t) determined by the planned individual movements TE as four times continuously time-differentiable position profiles s_(x)(t), s_(y)(t). In this manner, swinging and/or pendulum movements can be suppressed without having to rely on measurements of the load position P_(Z). It should be mentioned at this point that the use of trajectories that can be continuously differentiated even more often can ensure even smoother movement profiles that are even gentler on the drives.

To ensure that the position profiles s_(x)(t), s_(y)(t) defined by the specified individual movements TE are actually fourfold continuously differentiable, the position profiles s_(x)(t), s_(y)(t) can be filtered before they are executed. However, the described fourfold differentiability can also be achieved in a manner other than filtering, for example by polynomial approaches for the specified position, velocity and/or acceleration profiles. The filtering of individual movements TE, which are available as scalar progressions, is much easier than the filtering of multidimensional profiles. This is another reason why the use of individual movements TE represents a significant advantage in the control of lifting devices 1.

The described approach for generating flat trajectories by a suitable filtering or polynomial approach can also be used in a particularly advantageous manner to comply with the kinematic constraints for the lifting device drives mentioned further above as well as the geometric limitation of the deflection angle of the load. For example, the partial movements of the load 8 are related to the movement of the running element 5 via the known pendulum equations:

$x_{T} = {x_{L} + \frac{{\overset{¨}{x}}_{L}\left( {y_{T} - y_{L}} \right)}{{\overset{¨}{y}}_{L} + g}}$ $v_{T} = {{\overset{˙}{x}}_{L} - \frac{{{- {\overset{.}{y}}_{L}}{\overset{¨}{x}}_{L}} - {\left( {y_{T} - y_{L}} \right){\overset{...}{x}}_{L}}}{{\overset{¨}{y}}_{L} + g} - \frac{\left( {y_{T} - y_{L}} \right){\overset{¨}{x}}_{L}{\overset{¨}{y}}_{L}}{\left( {{\overset{¨}{y}}_{L} + g} \right)^{2}}}$ $a_{T} = {{\overset{¨}{x}}_{L} - \frac{{{\overset{¨}{y}}_{L}{\overset{¨}{x}}_{L}} + {2{\overset{˙}{y}}_{L}{\overset{...}{x}}_{L}} - {\left( {y_{T} - y_{L}} \right)x_{L}^{(4)}}}{{\overset{¨}{y}}_{L} + g} + \frac{{2{\overset{˙}{y}}_{L}{\overset{¨}{x}}_{L}{\overset{...}{y}}_{L}} - {2\left( {y_{T} - y_{L}} \right){\overset{...}{x}}_{L}{\overset{...}{y}}_{L}} - {\left( {y_{T} - y_{L}} \right){\overset{¨}{x}}_{L}y_{L}^{(4)}}}{\left( {{\overset{¨}{y}}_{L} + g} \right)^{2}} + \frac{2\left( {y_{T} - y_{L}} \right){\overset{¨}{x}}_{L}{\overset{...}{y}}_{L}^{2}}{\left( {{\overset{¨}{y}}_{L} + g} \right)^{3}}}$

The variables x_(T), v_(T), a_(T) here stand for the movements of the running element 5, x_(L) and y_(L) on the other hand for the coordinates of the load 8, whose corresponding derivatives are noted as {dot over (x)}_(L), {umlaut over (x)}_(L),

, x_(L) ⁽⁴⁾ and so on. According to the above, the given equations represent a flat parameterization of the state variables x_(T), v_(T), a_(T) as a function of the flat outputs x_(L), y_(L). The given relationship makes it clear that specifications regarding the profiles of the coordination x_(L) and y_(L) have a direct effect on the movement of the running element 5.

To implement the described filtering to generate flat trajectories, for example, a suitable filter F can be used, such as a moving-average filter (MA filter). A schematic representation of such filtering is shown in FIG. 3B. In this context, FIG. 3B shows a general filter F that takes position profiles s, velocity profiles v, and acceleration profiles a, and outputs filtered position profiles {tilde over (s)}, velocity profiles {tilde over (v)}, and acceleration profiles ã. The filter F can be designed to also output time derivatives of the mentioned variables, particularly of incoming acceleration profiles. The filter F can be designed as a single-input system, and only one of the mentioned variables position s, velocity v and acceleration a can be recorded and filtered and output again. However, the filter F can also be designed as a multiple-input system and process several variables simultaneously. In a known manner, the filter F may be implemented in the control unit 12.

The filter time τ_(filt) of a filter F implemented as an MA filter can be selected here in a particularly advantageous manner as a function of the geometry of the lifting device 1 and the pendulum equations. By selecting larger time constants, the previously planned individual movements can be filtered even more strongly and, for example, even more conservative progressions can be specified for the running element 5. By multiple filtering, individual movements TE can be generated in an extremely advantageous manner, by which kinematic constraints specified for the drives of the lifting device 1 are taken into account, such as speed, acceleration, jerk limitations.

FIG. 1 also shows the most relevant case in practice, where an obstacle 11 is located between the starting point A and the end point E. An obstacle 11 in this case can be another ship, a stack of containers 9 or any other obstacle 11. The obstacle 11 leads to the fact that no direct connection between the starting point A and the end point E, i.e., no trajectory T in the form of a straight line is possible. As will be shown in detail below, obstacles 11 can in many cases be taken into account in an advantageous manner by so-called prohibition zones V_(i), which enclose the obstacles 11 and which the load 8 must avoid during its movement, for example in order to avoid a collision or to ensure sufficient safety distance (the index i≥1 refers here to the number of prohibition zones V_(i)). Accordingly, a prohibition zone V_(i) may also be noticeably larger than an obstacle 11 encompassed by it. In an advantageous manner, a trajectory T can be designed according to the profile shown in FIG. 1 by the dashed line, i.e., substantially have a sufficiently smooth profile between starting point A and end point E, and bypass the prohibition zone V accordingly.

Depending on the field of application of the lifting device 1, various obstacles 11 may be arranged between the starting point A and the end point E. The number, type and design of the obstacles 11 plays only a subordinate role for the invention; for example, only a single obstacle 11 could be arranged, or several obstacles 11 of different sizes could be arranged, or there could be no obstacle 11 at all.

The prohibition zones V_(i), as well as the starting point A and the end point E, can either be defined manually by a user, e.g., via a suitable interface in the computing unit 12, or determined automatically by the computing unit 12. For this purpose, for example, a suitable laser scanning method can be used, which, for example, scans a working area 15 of the lifting device 1 and, in doing so, detects and measures obstacles 11 and transmits the determined data to the computing unit 12. Such methods are known in the prior art.

To define the prohibition zones V_(i), for example, an envelope of an obstacle 11 in the shape of a rectangle can be used, which completely includes the obstacle 11, as shown in FIG. 4 . Here, the height H_(R1) of the rectangle corresponds at least to the maximum extension of the obstacle 11 in Y-direction and the width W_(R1) of the rectangle corresponds at least to the maximum extension of the obstacle 11 in X-direction. This is only to be understood by way of example; of course, other geometric definitions of prohibition zone V₁ are also conceivable. In general, for example, a single prohibition zone V₁ may enclose multiple obstacles 11. However, a finer definition of multiple prohibition zones V_(j) may be applied, e.g., based on the specific outlines of the obstacles 11.

In the case of an obstacle 11 located between the position P_(Z) taken on by the load 8 at the command time point t_(k) and the new end point E_(n), a second individual movement TE_(Y2) can be planned in an advantageous manner for the second movement direction Y to move the load 8 around the obstacle 11. In the situation shown in FIG. 4 , this second individual movement TE_(Y2) provides for a lifting operation that first raises the load 8 to the point where a collision with the obstacle 11 can be ruled out.

In a situation such as that shown in FIG. 4 , the sequence in which the planned individual movements TE are executed is of decisive importance. As can be seen directly from FIG. 4 , starting from the command time point t_(k), a lowering movement in the Y-direction by the individual movement TE_(Y) may only be executed when a collision with the obstacle 11 can be ruled out. According to the invention, a so-called movement sequence is specified for this purpose, which determines sequence in which the specified individual movements TE are to be executed and the time points at which these individual movements TE are started.

A first possibility in this respect is to execute the planned individual movements TE at intervals from one another, i.e., to wait after executing an individual movement TE and only continue with the next individual movement TE corresponding to the movement sequence after a specified waiting time.

Specifically, a movement sequence can specify, for example, that in the situation shown in FIG. 4 , first a lifting movement TE_(Y2) is executed in the Y-direction as an individual movement (“Hoist Up”), then the vertical individual movement TE_(x) is executed in the X-direction (“Move Trolley”), and only then the individual movement TE_(Y1) is executed in the Y-direction as a lowering movement (“Hoist Down”). The waiting time between these individual movements TE_(X), TE_(Y), TE_(Y2) can be predefined or determined depending on the situation. For example, it is possible to wait until the individual movement TE_(Y2) is completed, and only after its completion to start the next individual movement TE_(X), either along the same movement direction X, Y or along a different movement direction X, Y. In this manner, however, time is lost due to the waiting times to be provided between the various individual movements TE_(X), TE_(Y), TE_(Y2). In an advantageous manner, the planned individual movements TE can also be executed overlapping in time for this reason.

Overlapping in time means here that, for example, an individual movement in the Y-direction is already started before an individual movement in the X-direction is completely finished. Such an overlap of individual movements TE can also be recorded in a movement sequence within the scope of the present invention.

In the course of determining the movement sequence in which the planned individual movements are to be executed, it is often particularly advantageous to additionally check whether a collision of the load 8 with a prohibition zone V_(i) may occur in the profile of the resulting replanning trajectory TU.

How to proceed in this respect is shown in FIGS. 5A-5C. FIG. 5A and FIG. 5B show on the one hand acceleration, velocity and position profiles (a_(x), v_(x), s_(x) and a_(y) v_(y), s_(y)) for the movement directions X and Y, as they can be used for replanning the movement of a load 8 according to the invention. In the situation shown, the load 8 is located to the left of an obstacle 11 at the command time point t_(K), as can be seen in FIG. 5C. Accordingly, the individual movements TE_(Y1), TE_(Y2) planned in the Y-direction can be adopted without restriction. Purely by a movement in Y-direction, starting from the position P_(z)(t_(k)), no collision can be caused.

In the X-direction, however, it can be seen that the individual movement TE_(Xa) would lead to a collision with the obstacle 11. The individual movement TE_(Xa) planned at the beginning (after replanning of the old, “a”) is shown in FIG. 5A by the dash-dotted progressions s_(xa), v_(xa) and a_(xa). In combination with the lifting movement TE_(Y2) planned for the Y-direction, the first replanning trajectory TU_(a) shown in FIG. 5C would result, which, however, would cause a collision with the prohibition zone V at the collision time t_(1X). For this reason, the individual movement TE_(Xa) initially planned for the X-direction is not executed and instead a braking operation is performed for a specified duration T_(St). The braking operation corresponds to the phase with negative acceleration provided at the beginning in FIG. 5A. Based on this, a new individual movement TE_(Xn) is planned in the X-direction, and is executed instead of the previously planned, old individual movement TE_(xa) at the end of the braking operation.

In a particularly elegant manner, a check as to whether a collision with an obstacle is to be expected can be performed in the following manner: Before the execution of at least one planned individual movement TE, so-called collision times t_(iX), t_(iY) are determined and compared with one another. The collision times t_(iX), t_(iY) are to be understood as the respective time points at which the load 8 would reach a projection S_(i)′ or S_(i)″ of a keypoint S_(i) derived from a prohibition zone V_(i) placed around an obstacle 11 on the respective movement direction X, Y by the respective planned individual movements TE_(X), TE_(Y).

Preferably, such keypoints S_(i) are, for example, the illustrated corner points of prohibition zones V_(i). In order to check whether an expected replanning trajectory TU would lead to a collision of the load 8 with an obstacle 11 specified in the working area 15, it can be checked in the situation shown in FIG. 5C whether the corresponding collision time t_(1X) for the individual movement TE_(Xa) along the X-axis lies before the corresponding collision time t_(1Y) for the individual movement TE_(Y2) along the Y-axis, i.e. t_(iX)<t_(iY) applies (specifically transferred to FIG. 5C, the inequality would be t_(1X)<t_(1Y)). In this case, a collision can be concluded in the situation shown in FIG. 5C. The corresponding collision times t_(ix), t_(iy) are shown in FIGS. 5A and SB.

In the procedure described, particular attention must be paid to the Y-coordinate of the load position P_(Z), i.e., the projection P_(Z)″ of the load position P_(Z) on the Y-axis. It must be taken into account whether the Y-coordinate P_(Z)″ of the load position P_(Z) at the beginning of an individual movement TE_(Y) in the Y-direction is larger or smaller than the projection S_(i)″ of the next keypoint S_(i) in the Y-direction onto the Y-axis. In many practically relevant cases, the load position P_(Z) at the beginning of a newly planned individual movement TE is given by the load position P_(Z) at command time point t_(k), i.e., P_(Z)(t_(k)). If the projection S_(i)″ of the keypoint S, closest in Y-direction to the Y-axis is smaller than the projection P_(Z)″ of the load position P_(Z) to the Y-axis, the condition for a collision is fulfilled exactly if vice versa t_(iY)<t_(iX) applies.

Individual movements TE_(X), TE_(y) are often not available in analytical form. In an advantageous manner, numerical root finding methods can also be used in such cases to determine the collision times t_(iX), t_(iY), such as the well-known bisection method or Newton's method.

In practical implementation, it is often advantageous to combine both analytical and numerical methods in order to determine the collision times t_(iX), t_(iY). Such a case is described below. The acceleration profiles a_(x) and a_(y) are initially specified as piecewise constant as described. For these piecewise constant acceleration profiles a_(x) and a_(y), the corresponding position profiles s_(x) and s_(y) can easily be calculated analytically. For the resulting analytical descriptions of the position profiles s_(x)(t) and s_(y)(t), the collision times t_(iX), t_(iY) can be calculated with little effort, e.g., by determining the zeros t_(x0), t_(y0) of the functions f_(x)(t)=s_(x)(t)−S_(i)′, f_(y)(t)=s_(y)(t)−S_(i)″. For these zeros t_(x0), t_(y0), accordingly f_(x)(t_(x0))=f_(y)(t_(y0))=0 is valid by definition. Of course, the formulas f_(x)(t) and f_(y)(t) can also take into account the height and width of the load 8, which are usually given by the height H₇ of the load receiving element 7 plus the height H₉ of a container 9 in the Y-direction, as well as half the width B₇ of the load receiving element 7 (typically corresponding to half the width B₉ of the container 9). Depending on whether the load 8 approaches the next keypoint S_(i) from the left, right, top or bottom, the function f_(x)(t), for example, can be increased or decreased by half the width B₉.

If the individual movements TE_(X), TE_(Y) are filtered, for example by an MA filter described at the beginning, the position profiles s_(x)(t) and s_(y)(t) in particular are filtered to form filtered position profiles {tilde over (s)}_(x)(t) and {tilde over (s)}_(y)(t). For such filtered position profiles {tilde over (s)}_(x)(t) and {tilde over (s)}_(y)(t), the property of an MA filter can now be utilized, according to which the zeros t_(x0), t_(y) determined from the function f_(x)(t) shown above can be shifted by filtering by a maximum of the filter time τ_(filt) of the MA filter used for filtering. Accordingly, for the case of twofold filtering, a time interval of length 2·τ_(filt) can be placed around the previously determined zeros t_(x0), t_(y0), with the zeros t_(x0), t_(y0) at the beginning of the interval at the left interval boundary. In such a time interval, a bisection procedure can now be used to search for zeros of the functions {tilde over (ƒ)}_(x)(t)={tilde over (s)}_(x)(t)−S′_(i) and {tilde over (ƒ)}_(y)(t)={tilde over (s)}_(y)(t)−S″_(i). These zeros then correspond to the sought collision times t_(iX), t_(iY) for the filtered position profiles {tilde over (s)}_(x)(t) and {tilde over (s)}_(y)(t).

Besides the described comparison of two collision times t_(iX), t_(iY), another approach for collision checking can be mentioned. Thus, initially only the collision time t_(iy) can be calculated, which indicates when a projection of a given keypoint S_(i)″ onto the Y-axis is reached along the Y-axis by a planned individual movement TE_(Y) in Y-direction. This collision time ty can also be used to determine the position s_(x)(t_(iy)), which describes the position on the X-axis specified by the planned individual movement TE, in the X-direction at the collision time t_(iy).

The check whether a collision with an obstacle 11 is to be expected due to planned individual movements TE can then be performed by comparing the position s_(x)(t_(iy)) with the projection Si′ of the keypoint Si on the X-axis. In the specific case shown in FIG. 5A-SC, for example, a collision can be concluded if one of the conditions s_(x)(t_(1y))>S₁′ or s_(x)(t_(2y))<S₂′ is fulfilled. Compared to the procedure described above, computing time can be saved because only one collision time t_(iy) has to be determined. This approach is indicated in FIG. 5A by the points s_(xa)(t_(1y)) and s_(xn)(t_(1y)). While s_(xa)(t_(1y)) is above the projection S₁′ (which would lead to a collision), s_(xn)(t_(1y)) is below the projection S₁′, with the desired effect of collision avoidance.

On the other hand, to check for a collision, it is also possible to first determine the collision time t_(ix), to use this collision time t_(ix) to determine the corresponding position on the Y-axis s_(y)(t_(ix)), and to compare the corresponding position on the Y-axis s_(y)(t_(ix)) with a projection Si″ of a keypoint Si on the Y-axis. In this sense, in the case shown in FIG. 5A-5C, a condition to be met for a collision would be s_(y)(t_(1x))<S₁″ (not shown).

Specifically, in order to check for a possible collision of the load 8 with an obstacle 11, prior to the execution of at least one individual movement TE, in the case shown the individual movement TE_(X), a check as described above, a so-called “verification step”, is performed. In the verification step, the expected replanning trajectory TU in the working area 15 determined by the at least one planned individual movement TE_(X) is determined.

If one of the above-mentioned advance calculations shows that a collision is to be expected, the individual movement TE causing the collision is not performed and instead a specified braking operation is performed along the movement direction X, Y for which the at least one non-performed individual movement TE is planned, in FIG. 5C the movement direction X. The braking operation is performed for at least the duration of a specified minimum braking time T_(St). After the minimum braking time T_(St), at least one individual movement TE that has not been executed is replanned to a new individual movement TE in a replanning step in an advantageous manner. In a further checking step with the at least one new individual movement TE, it can be checked again whether the replanning trajectory TU to be expected on the basis of the new individual movement TE leads to a collision. If no collision is detected, the newly planned individual movement TE can be executed. If, however, a collision of the load 8 with an obstacle 11 is predicted again in the preceding verification step, a specified braking operation can advantageously be performed again for at least one further minimum braking time T_(St). After that, a replanning step and a review step following this replanning step can be performed again.

The load 8 can also be brought to a complete standstill by repeatedly performing the braking operation described above. Further planning of individual movements TE then occurs starting from the standstill of the load 8. The possibility of using the method according to the invention to plan corresponding individual movements TE starting from the standstill of the load 8 and thus a trajectory resulting from these individual movements TE opens up the option of also planning fundamentally new trajectories T for the movement of a load 8 using the method according to the invention. If the load 8 is at standstill at the start of a movement operation and no trajectory is yet known for its movement from the starting point A to the end point E, the standstill at the starting point A can be assumed/specified as the end of a repeatedly executed braking operation and a trajectory for transferring the load 8 from standstill at the starting point A to the end point E can be planned by applying the method according to the invention.

Similar to the previously described determination of the collision times t_(ix), t_(iy), a time interval can also be specified for a braking operation in which the load 8 can be brought to a complete standstill. Specifically, the limits t_(k) (command time point) and t_(k)+T_(TE) can be specified for this time interval, where T_(TE) describes the duration of a planned individual movement TE. Within this time interval, the load 8 comes to a standstill when a braking operation is repeatedly executed, wherein the specific time point can be determined as before by a bisection method.

Although the present invention has so far been described in terms of a trajectory T in the X-Y plane E_(XY), it is also possible to extend it to a three-dimensional trajectory T in space. The basic method for replanning even three-dimensional trajectories T on the basis of preferably independent individual movements remains unchanged. If the load 8 is additionally moved along a third movement direction Z by the lifting device 1, at least one individual movement TE_(Z) is also planned for the third movement direction Z in order to replan the trajectory T in accordance with the method according to the invention, which is executed in accordance with a specified movement sequence in addition to the individual movements TE_(X), TE_(Y) planned for the first movement direction X and for the second movement direction Y.

For the application of the present invention in the planning of three-dimensional trajectories, it is in many cases advantageous to specify a 3D working area for constraining the movement of the load 8 instead of a two-dimensional working area 15. In contrast to a purely two-dimensional consideration, however, it may also be necessary in the 3D case to take into account the extent of an obstacle 11 as well as the extent of a load 8 in the Z direction. This may be necessary, for example, in assembly halls where obstacles 11 arranged on the walls project into the space of the assembly hall. In such cases, situations may arise in which an obstacle 11 can also be avoided by suitable lowering movements, but this can also be implemented by the method according to the invention.

Such a case is shown in FIG. 6 , where, as in the previous examples, new individual movements TE_(X1), TE_(X2), TE_(Y1), TE_(Y2), TE_(Y3) are planned at command time point tk, starting from position P_(z)(t_(k)). The important case is shown that several individual movements TE_(X1), TE_(X2) are also planned in the X-direction, which is equally possible within the scope of the present invention. In FIG. 6 , for example, the obstacle 11 a is avoided by a lifting movement TE_(Y3) and the obstacle 11 b is avoided by a lowering movement TE_(Y2). The final transfer to the end point E is performed by a final lifting movement TE_(Y1).

In many practical applications, it can be advantageous in this context to use optical measuring systems to detect the load position P_(Z) or also obstacles 11, as described for example in EP 3 653 562 A1. Optical measuring systems include suitable camera systems in particular, but also laser scanners. For the purpose of monitoring obstacles 11 that change with respect to their position in the working area 15, a camera can be mounted/installed directly on the trolley of a lifting device 1. Specifically, an optical detection of obstacles can in many cases provide information about how high and at which spatial positions obstacles 11 to be avoided are located. If a change in the position of an obstacle 11 is detected, a new prohibition zone V can be derived from it and the replanning of a trajectory for the movement of a load can be performed as described. In addition to camera and/or laser scanning systems, other approaches to detecting obstacles 11 are also conceivable. In many cases, automation or logistics systems implemented in software also provide information about obstacles to be considered.

A further application for which the method of trajectory planning according to the invention is particularly suitable are so-called bulk material cranes. Due to the fact that in an advantageous embodiment of the method according to the invention quadruple differentiable flat trajectories can be planned, undesired load swinging can be excluded by principle. In the case of bulk material cranes, this feature is of particular importance, as it reliably prevents possible losses of transported bulk material. In addition, by preventing the swinging, the mechanical stress on crane structure and the danger posed by swinging loads to personnel can also be effectively reduced. In manner, a position measuring unit, which is usually required for bulk material cranes to suppress load swinging, can be dispensed with.

In the case of bulk material cranes, there is also a further advantageous application of the method according to the invention. Thus, for unloading bulk material, an unloading area can be defined in which bulk material is to be unloaded from a gripper. Using the method according to the invention, an unloading operation can then be performed as follows: First, a trajectory T is planned from the starting point A, where the gripper has been filled, to a specified end point E in the unloading area where the gripper is to be emptied. Then, during the movement of the gripper from the starting point A to the end point E_(n), the replanning functionality according to the invention is used to reverse the load movement in the unloading area (reversal point). This can be achieved by specifying a new end point E_(n), preferably located in the vicinity of the starting point A. This prevents the gripper, i.e., the load 8, from coming to a standstill during the entire unloading process and allows the unloading of the gripper to take place vertically above the unloading area during the movement. This saves time during the entire movement sequence that would otherwise be needed to stop the gripper at the original end point E and accelerate again in the opposite direction.

It is noted that the foregoing examples have been provided merely for the purpose of explanation and are in no way to be construed as limiting of the present invention. While the present invention has been described with reference to an exemplary embodiment, it is understood that the words which have been used herein are words of description and illustration, rather than words of limitation. Changes may be made, within the purview of the appended claims, as presently stated and as amended, without departing from the scope and spirit of the present invention in its aspects. Although the present invention has been described herein with reference to particular means, materials and embodiments, the present invention is not intended to be limited to the particulars disclosed herein; rather, the present invention extends to all functionally equivalent structures, methods and uses, such as are within the scope of the appended claims. 

1. A method for controlling a lifting device which moves a load along a first movement direction and along a second movement direction within a specified working area of the lifting device in accordance with a specified trajectory from a starting point to an end point, wherein at a command time point during the movement of the load, the end point is changed to a new end point, wherein, taking into account specified kinematic constraints of the lifting device, an individual movement is planned for the first movement direction and for the second movement direction respectively, which individual movement determines the further movement of the load along the respective movement direction from the command time point onwards, wherein the individual movements each end in a projection of the new end point onto the respective movement direction, and wherein the planned individual movements are executed in accordance with a specified movement sequence in order to move the load further along the first movement direction and further along the second movement direction in accordance with a replanning trajectory resulting from the movement sequence of the planned individual movements.
 2. The method according to claim 1, wherein the individual movements planned for the first movement direction and for the second movement direction are planned as individual movements that are independent of one another.
 3. The method according to claim 1, wherein the planned individual movements each comprise a position profile that can be continuously differentiated at least four times in time.
 4. The method according to claim 3, wherein the position profiles for generating the temporally at least four times continuous differentiability are filtered by a filter with a specifiable time constant.
 5. The method according to claim 4, wherein the time constant of the filter is selected as a function of the geometry of the lifting device in order to comply with the specified kinematic constraints of the lifting device in a combined execution of the individual movements.
 6. The method according to claim 1, wherein, in the case of an obstacle located between the position taken on by the load at the command time point and the new end point, a further individual movement is planned for the second movement direction which in combination with the individual movement planned along the first movement direction moves the load around the obstacle, and wherein the second individual movement is executed in accordance with the specified movement sequence before the individual movement already planned for the second movement direction.
 7. The method according to claim 1, wherein the movement sequence is specified such that individual movements along the first movement direction and individual movements along the second movement direction are started alternately.
 8. The method according to claim 1, wherein the movement sequence is specified such that an individual movement along the first movement direction and an individual movement along the second movement direction are executed overlapping in time.
 9. The method according to claim 1, wherein, before the execution of at least one planned individual movement, it is checked whether the expected replanning trajectory leads to a collision of the load with an obstacle specified in the working area.
 10. The method according to claim 9, wherein, in order to check whether the expected replanning trajectory leads to a collision of the load with an obstacle specified in the working area, projections of a keypoint derived from the specified obstacle onto the movement directions are determined, wherein a collision time is determined at which the load reaches the projection onto the first movement direction with the individual movement planned for the first movement direction, and a collision time is determined at which the load reaches the projection onto the second movement direction with the individual movement planned for the second movement direction, and wherein the determined collision times are compared with one another.
 11. The method according to claim 9, wherein, in order to check whether the expected replanning trajectory leads to a collision of the load with an obstacle specified in the working area, a projection of a keypoint derived from the specified obstacle onto one of the movement directions is determined, wherein a collision time is determined at which the load reaches the determined projection with the individual movement planned for this movement direction, wherein a position of the load on the other movement direction take on by the load at the determined collision time is determined, and wherein the determined position is compared with a projection of the keypoint onto the movement direction for which the position of the load was determined.
 12. The method according to claim 10, wherein the collision times are determined using a root finding method.
 13. The method according to claim 10, wherein, in the event of a determined collision with an obstacle, the at least one individual movement is not executed, and wherein instead a specified braking operation is performed for at least the duration of a specified minimum braking time along that movement direction for which the at least one individual movement that was not executed had been planned.
 14. The method according to claim 13, wherein instead of the at least one individual movement which has not been executed, a new individual movement is planned for the corresponding movement direction, wherein it is checked whether the replanning trajectory resulting from the newly planned individual movement leads to a collision of the load with an obstacle specified in the working area, and wherein the new individual movement is executed if no collision is detected, or wherein the specified braking operation is continued for at least one further minimum braking time and a replanning of an individual movement and a check of the replanning trajectory resulting from the replanned individual movement are performed again if a new collision with an obstacle is detected.
 15. The method according to claim 1, wherein the position of the load is measured and is used for planning and/or executing the individual movements.
 16. The method according to claim 1, wherein the load is additionally moved along a third movement direction by the lifting device, wherein the load is moved within a specified 3D working space in accordance with a three-dimensional trajectory and wherein, for replanning the trajectory, at least one individual movement is also planned for the third movement direction and is executed in accordance with a specified movement sequence in addition to the individual movements planned for the first movement direction and for the second movement direction.
 17. A lifting device for moving a load from a starting point to an end point in accordance with a specified trajectory within a specified working area of the lifting device, wherein a load receiving element is provided in the lifting device for receiving the load which is connected by at least one retaining element to a running element, wherein the running element is movable along a first movement direction by a running element drive and the load receiving element is movable along a second movement direction by a lifting drive, wherein a computing unit is provided in the lifting device, which computing unit is designed to read in at a command time point during the movement of the load (8) a new end point specified in the working area for replanning the trajectory, wherein the computing unit is further configured to plan, taking into account specified kinematic constraints of the lifting device, an individual movement for the first movement direction and for the second movement direction respectively which define the further movement of the load along the respective direction of movement from the command time point onwards, wherein the individual movements each end in a projection of the new end point onto the respective direction of movement, and wherein the computing unit is configured to control the running element drive and the lifting drive of the lifting device in order to execute the planned individual movements in accordance with a specified movement sequence and thus to move the load further along the first movement direction and further along the second movement direction in accordance with a replanning trajectory resulting from the movement sequence of the planned individual movements. 